Impossible figures brought to life in virtual worlds

Ever found a computer game truly impossible? If not, you soon might, thanks to Chinese computer scientists who have found a way to depict physically impossible figures in 3D virtual environments.

The endless staircases of the Dutch artist M. C. Escher appear impossible and possible at the same time, and able to go in all directions. Such visual trickery depends heavily on the observer’s viewpoint – and that makes it difficult to animate Escher-type figures in games. If the viewpoint pans around a 3D computer depiction of such a staircase, “the impossibility is lost”, says Tai-Pang Wu at the Chinese University of Hong Kong.

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Now his team has found a way to make these images viewable from a useful array of angles. The trick is to take advantage of the image’s strangeness; viewers scarcely notice if an Escher staircase becomes slightly distorted.

So Wu’s team has written 3D software that deforms the impossible figures by a different amount for each viewing angle to maintain the illusion of impossibility. “We model the shape as if it’s a non-rigid body, like an amoeba, which can be deformed,” says Wu.

The right viewpoint

They also identify the range of angles for which impossibility – is maintained, and the software limits viewpoints to lie within that range. Wu thinks that the system could be incorporated into a graphics package for multimedia artists.

Impossible figures have been used in games before, though not in full 3D with panning camera motion. For instance, in 2000, the hit Blizzard Entertainment game Diablo II had a level set in an impossible piece of architecture. “But you couldn’t view the architecture from a different viewpoint,” Wu says.

“People love visual illusions and tricks and this is certainly an interesting geometric exercise,” says Daniel Cohen-Or of Tel Aviv University in Israel. But it is far from certain that game makers or graphics firms need such tools, he adds. “Finding a practical, commercial application will be tricky.”